Quick and accurate modeling of transmitted field

ABSTRACT

Systems and techniques to quickly and accurately model a transmitted electromagnetic field through a mask, to design a mask, and to create a library of corrections including edge corrections, edge-to-edge corrections, and corner corrections.

BACKGROUND

Electronic devices may be formed by patterning successive layers on asubstrate using lithography. The patterns are formed using an imagingplate such as a mask or reticle that is designed to produce the desiredfeatures on the substrate. As device feature sizes decrease, morecomplex mask designs are used.

For example, masks incorporating phase shift technology (referred to asphase shift masks) may be used to pattern small features. In a non-phaseshift mask, the light transmitted through adjacent features is in phase,so that between adjacent features the amplitude of the light addstogether. In a phase shift mask, light transmitted through adjacentfeatures may be phase shifted so that between the features the amplitudeof the light from one feature is about equal to but opposite in sign tothe amplitude of the light from the other feature. This destructiveinterference may allow greater control over the creation of smallfeatures.

Mask design may be performed using software. For complex mask designs(e.g., design of phase shift masks for sub-wavelength features),accurate mask design software may be undesirably slow. In contrast,faster mask design software may not be suitably accurate.

A number of different methods may be used by the software to designmasks. For example, a method referred to as a thin mask method usesgeometrical optics to calculate the transmitted field, ignoring lightscattering effects due to mask features. A boundary layer methodmodifies the thin mask field in feature edge areas (the so-calledboundary layer) to account for some scattering effects. The edge domaindecomposition method adds edge scattering corrections to the thin maskfield to improve the accuracy.

DESCRIPTION OF DRAWINGS

FIG. 1 is a cross-sectional side view of an isolated edge in a mask anda plot of the transmitted field.

FIG. 2 is a flowchart illustrating a method to design a mask to quicklyand accurately generate desired features onto a substrate.

FIG. 3 illustrates one way to synthesize the near-field.

FIG. 4 is an embodiment of a system for creating a mask.

FIG. 5 is a cross-sectional side view of an isolated space in a mask anda plot of the transmitted field.

FIG. 6 is a flowchart for calculating an entry in the library ofcorrections.

FIG. 7 is an embodiment of a system to generate a library ofcorrections.

Like reference symbols in the various drawings indicate like elements.

DETAILED DESCRIPTION

Systems and techniques described herein may allow for relativelyaccurate and fast mask design.

The first stage in mask design may involve identifying the desiredfeatures to be etched onto a substrate. The mask designer then creates amask that he thinks will produce these desired features. To model thefeatures that would result from applying the mask, the designer modelsthe pattern of the electromagnetic (EM) field transmitted through themask. Based on a comparison of the modeled features to the desiredfeatures, the designer may change his mask and repeat this process.

A key part of this process is the modeling of the transmitted EM field.A more accurate model of the EM field leads to a mask that moreaccurately produces the desired features.

Many rigorous methods exist to accurately determine the transmitted EMfield. For example, in the Finite Difference Time Domain method, theMaxwell equations are replaced by a set of finite difference equationsobtained by discretizing the Maxwell equations in space and time. Theyare essentially relationships between current states and the states ofthe next time step. The problem is then solved by marching the solutionsin time.

Another rigorous method, the Waveguide method, is a frequency domainmethod in which the simulation area is divided into 2D or 3D rectangularblocks. The material is considered uniform throughout each block so thatthe Maxwell equations can be solved analytically for each block.Solutions of all blocks are related by boundary conditions, which resultin a set of linear algebraic questions that are then solved using matrixmethods.

However, the computation time associated with applying these or otherrigorous methods to model transmitted EM field is prohibitive. Becauseof this difficulty, many mask designers employ a so-called “fastmethod.” For example, in the geometric optics method, the amplitude ofthe transmitted EM field in portions where the mask is chrome (or otherlight-blocking material) is considered to be zero. Where the mask isglass (or other light-passing material), the field is considered to beequivalent to the EM source. Although this method is simply and quicklycalculated, it ignores some of the physics of EM field transmission,such as diffusion around edges and interferences that may be caused bynearby features.

FIG. 1 illustrates this concept. The mask 100 is of an isolated edge 105that has a glass portion 110 and a light-blocking chrome portion 120. Inthe figure, light is transmitted through the mask in the direction shownby the arrow 130. Plot 140 shows the geometric optics model of thenear-field, and plot 150 illustrates a calculation of the near-fieldusing a rigorous method. A comparison of the two plots demonstrates thatthere is a certain amount of error associated with using a fast methodto determine the near-field. This error is indicated by the shadedportions 160. (Note that all the plots in the attached figures indicateamplitude only, not phase.)

Because fast methods only approximate the transmitted EM field, they mayresult in masks that do not accurately create the desired features. Arigorous model alternative, however, may allow accurate masks but themodel may be too computationally intensive for practical use. Thepresent approach offers a both fast and accurate way to model thetransmitted EM field and thereby to design an accurate mask.

The flowchart in FIG. 2 illustrates a method to design a mask to quicklyand accurately generate desired features onto a substrate. In block 210,the desired features are identified. Based on these features, a bestestimate mask is designed in block 220. A mask may consist of acombination of edges, corners, spaces, and other shapes; these shapesmay be referred to as primitives. In block 230, the mask isdeconstructed into its primitives. The corrections corresponding to theprimitives are retrieved from the corrections library in block 240.These corrections are used in block 250 to synthesize the near-field.This will be discussed in more detail below. In block 260, a simulationis conducted using the synthesized field to determine the features thatwould be generated by using the mask. The simulated features arecompared to the desired features in block 270 to determine whether thesimulated features are sufficiently similar to the desired features thatthe mask should be used without further modification. If so, the processends in block 280. If not, the mask is modified in block 290 to try togenerate features that are closer to the desired features. The processthen loops back to block 230 to analyze the modified mask.

FIG. 3 illustrates one way to accomplish the synthesis of block 250.First, the mask layout is used to construct a geometric field in block310. The edge corrections from the corrections library are added to thisgeometric field in block 320. Edge-to-edge corrections from the libraryare then added in block 330 and corner corrections are added in block340. The resulting synthesized field corresponds to the field that wouldresult from using a rigorous method. These corrections are discussed inmore detail below in connection with the creation of the library.

FIG. 4 shows a system for creating a mask according to an embodiment. Amask manipulator module 410 is coupled to a user input module 420, adisplay module 430, a mask deconstructor 440, an EM field synthesizer450, a feature calculator 460, a feature comparator 470, and a libraryof corrections for primitives 480.

An initial mask is input into the mask manipulator 410 and the maskdeconstructor 440 deconstructs the mask into its primitives (e.g.,edges, edge-to-edge interactions, corners, etc.). The EM fieldsynthesizer 450 looks up the correction for each primitive in thelibrary of corrections 480 and then applies these corrections to anappropriate fast method. The resulting synthesized field corresponds tothe field that would be calculated using a rigorous method. This isdiscussed in more detail below in connection with the creation of thelibrary.

The feature calculator 460 uses the synthesized field to determine thefeatures that would result from the application of the mask. The featurecomparator 470 then compares these features with the desired features.The mask manipulator 410 changes the mask to reduce the discrepancybetween the desired features and the synthesized features, and theresulting new mask is analyzed in the same way as described above.

The display 430 may show the synthesized field as well as the results ofthe comparison done by the feature comparator 470. If any user input isrequired, it may be given using the user input module 420.

Various tasks may be performed manually or automatically. For example,the feature comparator 470 may perform its comparison automatically orwith input from the user. A user may deconstruct a mask manually insteadof allowing the mask deconstructor 440 to do so automatically.Similarly, the mask manipulator 410 may make changes to a maskcompletely automatically or with some user interaction. (These aremerely non-exhaustive examples of tasks that may be performed withvarying degrees of automation.)

If there is no correction for a particular primitive on the mask in thelibrary, the correction for that primitive may be interpolated fromsimilar primitives. For example, suppose a mask has a space that is 25nm wide, but the closest corrections in the library are for spaces 20 nmand 30 nm wide. The correction for a 25 nm space may then be estimatedas, for example, a linear interpolation between the 20 nm correction andthe 30 nm correction. If the library contains primitives of sufficientnumber and variety, then interpolation may not introduce significanterror.

One important advantage of designing a mask as described above is thatvery small channels may be created. This results from the maskdesigner's ability to now quickly and accurately model the interactionbetween two edges that may be close together. Accordingly, in oneembodiment, channels may be designed and implemented that are of a widthequal to or less than the wavelength of the light being used.

In an embodiment, a simulated printed pattern generated for a maskdesign may be used to inspect a mask including the mask design. Masksmay also be generated using lithography techniques, and may acquiredefects during the manufacturing process or from contamination. The maskmay be inspected by comparing an actual printed pattern generated usingthe mask to the simulated printed pattern generated for the mask design.Any deviations between the simulated and actual printed patterns mayindicate a defect on the mask.

Creating a Library of Corrections

The library of corrections comprises entries that reflect the errorassociated with using a fast model instead of a rigorous method todetermine the transmitted EM field. For example, the shaded portions 160in FIG. 1 indicate the error associated with using a geometric modelinstead of a rigorous method to calculate the transmitted field for anisolated edge. This error may be calculated by subtracting the geometricmodel from the rigorous calculation. This quantity is called the “edgecorrection” because the addition of the quantity to the geometric model“corrects” it to conform to the rigorous model.

Similarly, an edge-to-edge interaction correction can be calculated.FIG. 5 represents an isolated pair of edges 505 and 507 in a mask 500.The mask has a light-transmitting portion 510 and a light-blockingportion 520. Light is directed into the mask in the direction shown byarrow 530. Plot 540 illustrates the geometric model of the amplitude ofthe transmitted field, and plot 550 represents the transmitted fieldcalculated using a rigorous method. The shaded portion 560 representsthe error associated with using the geometric model rather than arigorous method. To calculate an edge-to-edge interaction correction,the geometric field and the edge corrections are subtracted from therigorous field. The edge corrections are subtracted to isolate the errorassociated with the interaction of the edges. Reconstruction of therigorous field then involves adding both the edge corrections and theedge-to-edge interaction corrections to the geometric field.

Alternatively, a space correction may be calculated. In one embodiment,this involves subtracting only the geometric field from the rigorousfield. The resulting space correction is represented by the shadedregion 560. Reconstructing the rigorous field would then involve addingonly the space correction to the geometric field; no other edgecorrections would be required (for this isolated space). Such a spacecorrection may be used in place of separate edge corrections andedge-to-edge interaction corrections. In another embodiment, spacecorrections may be calculated as the sum of: (a) the average of the edgecorrections on each side of the space, and (b) the edge-to-edgeinteraction correction between the two edges. The space correction forthe space located beyond the edge at the end of a mask may be calculatedas one-half the edge correction for that edge.

To extend this further, a corner correction may be calculated bysubtracting the geometric field and the edge corrections of an isolatedcorner from the rigorous field of the isolated corner.

There are numerous shapes for which corrections may be calculated. Forexample, a particular square shape may be a shape for which it may beuseful to have a correction present in the library. A correction may becalculated that allows a quick and accurate synthesis of the rigorousfield.

Corrections more advanced than edge corrections, such as spacecorrections, corner corrections, and shape corrections, may account forscattering effects and interactions between mask features, which may beimportant for sub-wavelength features.

FIG. 6 shows a flowchart for calculating an entry in the library ofcorrections. Block 610 starts with a primitive shape, e.g., an isolatededge. The rigorous and geometric fields are calculated in blocks 620 and630, respectively. In block 640, the geometric field is subtracted fromthe rigorous field. Block 650 involves checking whether there are anymore basic primitives than :he primitive shape under consideration. Forexample, the edges surrounding a space are more basic primitives thanthe space itself. If there are such more basic primitives, thecorrections for those primitives are subtracted in block 670 from theresult of block 640; the result of block 670 is then entered in:o thelibrary in block 680 as the correction for the primitive shape underconsideration. If there were not any more basic primitives in block 650,the result of block 640 is entered into the library in block 660.

The correction for each primitive may vary depending on many differentparameters. Thus, each correction may be calculated for severaldifferent values of the various parameters. These parameters may beformulated into an index to aid in retrieving entries from the library.For example, corrections may be dependent on one or more of thefollowing: illumination wavelength; glass material refractive index andextinction coefficient; absorber material refractive index; extinctioncoefficient; stack thickness; and glass phase trench side wall profileand undercut. In addition, an edge library may be dependent onadditional parameters, such as light polarization; phase/chrome on theleft side of the edge; and phase/chrome on the right side of the edge.Similarly, an edge-to-edge interaction library may have additionaldependencies on: light polarization; width between the two edges;phase/chrome on the left; phase/chrome in the middle; and phase/chromeon the right. This idea may be extended for libraries for other shapes,such as corners, which may be dependent on one or more of the following:light polarization; lower left phase/chrome; upper left phase/chrome;lower right phase/chrome; and upper right phase/chrome.

Additional observations may allow some libraries to be created bymanipulating other libraries. For example, a particular primitive may bethe mirror image of a second primitive for which a library alreadyexists. In that case, a library for the first primitive may be generatedas a mirror image of the library for the second primitive. Similarly, aprimitive may be a 90-degree clockwise geometric rotation of anotherprimitive; an entirely new library may be created simply by rotatingclockwise an existing library. Thus, performing some operations, such asthe geometric operations of mirror image, rotation, etc., may allowlibraries of corrections to be generated without the need to fullycalculate each library from scratch. This may reduce the time requiredto generate the libraries.

An advantage of calculating a library of corrections is that the longcomputation time associated with using rigorous methods may be performedbefore the mask-design process has even begun. The rigorous field(synthesized by adding the appropriate corrections to a fast method) maythen be used during the design process without the delay involved withcalculating the rigorous field itself. Moreover, the one-time investmentin computation time to create the library of corrections may allow forthe unlimited use of those corrections to synthesize the rigorous fieldin the design of future masks. Thus, once a rigorous method is used toconstruct the library, calculating the transmitted EM field is simply amatter of choosing the correct corrections from the library and applyingthese corrections to a fast method. The fast method used in synthesizingthe field using the corrections may be the same fast method that wasused in creating the corrections.

FIG. 7 shows an embodiment of a system to generate a library ofcorrections. A library generator module 710 is coupled to a user inputmodule 720, a display module 730, a parameters database 740, a rigorousfield generator 750, a fast field generator 760, a primitives database770, and a library of corrections for primitives 780.

The library generator 710 selects a primitive from the primitivesdatabase 770 and a set of parameters from the parameters database 740.These are used by the rigorous field generator 750 to generate a modelof the transmitted field using a rigorous method. Likewise, the fastfield generator 760 may use the same quantities to generate a model forthe transmitted field using a fast method, such as the geometric opticsmethod. The library generator 710 then subtracts the fast field from therigorous field. Additionally, if there are any corrections for morebasic primitives in the library 780, the library generator alsosubtracts those corrections from the rigorous field. The resultingcorrection is stored as an entry in the library 780. This entry may beindexed according to the values that were used from the parametersdatabase 740 and the primitives database 770.

A number of implementations have been described. Nevertheless, it willbe understood that various modifications may be made without departingfrom the spirit and scope of the invention. For example, the library isnot limited in the types of corrections present; it should be evidentthat there are many other types of corrections that may be in thelibrary (e.g. space corrections, corner-to-corner interactioncorrections, etc.). Also, blocks in a flowchart may be skipped orperformed out of order and still provide desirable results. Accordingly,other implementations are within the scope of the following claims.

1. An apparatus comprising: a mask deconstructor to deconstruct at leasta portion of a mask pattern into a plurality of primitives; a library ofcorrections including a plurality of corrections having been generatedusing a rigorous method, said plurality of corrections including edgecorrections and at least one of corner corrections, space corrections,shape corrections, and edge-to-edge corrections, wherein each correctionof said plurality of corrections comprises a difference of a rigorousfield and a fast field; and an electromagnetic field synthesizerconfigured to apply the retrieved corrections to the primitives tosynthesize a near-field corresponding to said at least a portion of themask.
 2. The apparatus of claim 1, further comprising: a featurecalculator to simulate a printed pattern corresponding to said at leasta portion of the mask pattern using the synthesized near-field.
 3. Theapparatus of claim 2, further comprising: a feature comparator tocompare the simulated printed pattern to a desired printed pattern. 4.The apparatus of claim 3, further comprising: a mask manipulator tomodify the mask pattern in response to the simulated printed patternsubstantially deviating from said desired printed pattern.
 5. Theapparatus of claim 2, further comprising: a mask inspector to inspect amask including said at least a portion of the mask pattern by comparingthe simulated printed pattern with a printed pattern generated usingsaid mask.
 6. The apparatus of claim 1, wherein the mask patternincludes a plurality of features, said features including featuressmaller than a wavelength of light with which the mask is to beilluminated.
 7. The apparatus of claim 1, wherein said electromagneticfield synthesizer is further configured to apply the retrievedcorrections to the primitives using a fast method.
 8. The apparatus ofclaim 1, wherein said electromagnetic field synthesizer is furtherconfigured to: construct a geometric field corresponding to said atleast a portion of the mask pattern; add edge corrections to thegeometric field; and add corner corrections to the geometric field. 9.The apparatus of claim 1, wherein said electromagnetic field synthesizeris further configured to: construct a geometric field corresponding tosaid at least a portion of the mask pattern; add edge corrections to thegeometric field; and add edge-to-edge interaction corrections to thegeometric field.
 10. The apparatus of claim 9, wherein saidelectromagnetic field synthesizer is further configured to add cornercorrections to the geometric field.